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Let H be the set of all points of the form (s, s-1). Determine whether H is a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy. Property 1: Contains zero vector Property 2: Closed under vector addition Property 3: Closed under multiplication by scalars Determine which of the following sets is a vector space. V is the line y = x in the xy - plane: V W is the union of the first and second quadrants in the xy-plane: W = * : y zo } U is the line y = x + 1 in the xy - plane: U = IM :V=X+1 Let H be the set of all points in the xy - plane having at least one nonzero coordinate: x, y not both zero . Determine whether H is a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy: Property 1: Contains zero vector Property 2: Closed under vector addition Property 3: Closed under multiplication by scalars If the set W is a vector space, find a set S of vectors that spans it. Otherwise, state that W is not a vector space.. a - 4b] W is the set of all vectors of the form 5 4a + b where a and b are arbitrary real numbers. - a - b If the set W is a vector space, find a set S of vectors that spans it. Otherwise, state that W is not a vector space. a + 6b] W is the set of all vectors of the form 3b 4a - b , where a and b are arbitrary real numbers. - a Prove that the set W is a vector space by finding a matrix A such that W = Col A. 2r - t Otherwise, state that W is not a vector space. W = 4r - s + 4t s + 2t : r, s, tin Ry - 4s + t